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Feasible generalized least squares estimation of multivariate GARCH(1, 1) models

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  • Poloni, Federico
  • Sbrana, Giacomo

Abstract

We provide a feasible generalized least squares estimator for (unrestricted) multivariate GARCH(1, 1) models. We show that the estimator is consistent and asymptotically normally distributed under mild assumptions. Unlike the (quasi) maximum likelihood method, the feasible GLS is considerably fast to implement and does not require any complex optimization routine.

Suggested Citation

  • Poloni, Federico & Sbrana, Giacomo, 2014. "Feasible generalized least squares estimation of multivariate GARCH(1, 1) models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 151-159.
    • Handle: RePEc:eee:jmvana:v:129:y:2014:i:c:p:151-159
    DOI: 10.1016/j.jmva.2014.04.015
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    References listed on IDEAS

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    1. Sbrana, Giacomo & Poloni, Federico, 2013. "A closed-form estimator for the multivariate GARCH(1,1) model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 152-162.
    2. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, November.
    3. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    4. Kristensen, Dennis & Linton, Oliver, 2006. "A Closed-Form Estimator For The Garch(1,1) Model," Econometric Theory, Cambridge University Press, vol. 22(2), pages 323-337, April.
    5. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    6. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    7. Christian Hafner & Helmut Herwartz, 2008. "Analytical quasi maximum likelihood inference in multivariate volatility models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 219-239, March.
    8. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 26-54.
    9. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    10. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
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    Cited by:

    1. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.

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